Stellar Centre Research Articles

Compact anisotropic stellar distribution with linear barotropic equation of state in energy–momentum trace coupling modification of general relativity

There are no known exact isotropic or anisotropic stellar models with an equation of state in energy–momentum trace-coupling (EMTC) modifications of general relativity — the simplest linear case of f(R,T) gravity. The difficulty lies in the intricate entanglement of the density and pressure functions that generate intractable governing equations when an equation of state is introduced. For example there is no interior Schwarzschild incompressible star analogue in the well studied f(R,T) theory. In Einstein’s theory it is straightforward to find anisotropic stellar models with a linear equation of state since the system is under-determined and there remains one more choice to nominate any of the variables. This is also true in EMTC theories however, the master field equation is more formidable. If interpreted as a linear second order equation, no viable solutions emerge by prescribing one of the gravitational potentials or by suppressing some terms in the spirit of Tolman (1939). Rewriting as a nonlinear first order equation and speculating on a power-law form of the temporally directed gravitational potential results in success in finding a physically viable compact star distribution. Specifically the model has monotonic decrease of both pressure and density and a surface of vanishing pressure exists. Several stability tests are imposed and the model performs according to expectations. The singularity at the stellar center may be cured by insertion of a regular core enveloped by our fluid model in a multi-layered star.

New DA white dwarf models for asteroseismology of ZZ Ceti stars

Context. Asteroseismology is a powerful tool used to infer the evolutionary status and chemical stratification of white dwarf stars and to gain insights into the physical processes that lead to their formation. This is particularly true for the variable hydrogen-rich atmosphere (DA) white dwarfs, known as DAV or ZZ Ceti stars. They constitute the most numerous class of pulsating white dwarfs. Aims. We present a new grid of white dwarf models that take into account advances made over the last decade in modeling and input physics of both the progenitor and the white dwarf stars. As a result, it is possible to avoid several shortcomings present in the set of white dwarf models employed in the asteroseismological analyses of ZZ Ceti stars that we carried out in our previous works. Methods. We generate white dwarf stellar models appropriate for ZZ Ceti stars with masses from ∼0.52 to ∼0.83 M⊙, resulting from the whole evolution of initially 1.5–4.0 M⊙ mass star models. These new models are derived from a self-consistent way with the changes in the internal chemical distribution that result from the mixing of all the core chemical components induced by mean molecular-weight inversions, from 22Ne diffusion, Coulomb sedimentation, and from residual nuclear burning. In addition, the expected nuclear-burning history and mixing events along the progenitor evolution are accounted for, in particular the occurrence of third dredge-up, which determines the properties of the core and envelope of post-AGB and white dwarf stars, as well as the white dwarf initial-final mass relation. The range of hydrogen envelopes of our new ZZ Ceti models extends from the maximum residual hydrogen content predicted by the progenitor history, log(MH/M⊙)∼ − 4 to −5, to log(MH/M⊙) = − 13.5, thus allowing for the first stellar models that would enable the search for seismological solutions for ZZ Ceti stars with extremely thin hydrogen envelopes – if, indeed, they do exist in nature. We computed the adiabatic gravity(g)-mode pulsation periods of these models. Calculations of our new evolutionary and pulsational ZZ Ceti models were performed with the LPCODE stellar evolution code and the LP-PUL stellar pulsation code. Results. Our new hydrogen-burning post-AGB models predict chemical structures for ZZ Ceti stars that are substantially different from those we used in our previous works, particularly in connection with the chemical profiles of oxygen and carbon near the stellar centre. We also discuss the implications of these new models for the pulsational spectrum of ZZ Ceti stars. Specifically, we find that the pulsation periods of g modes and the mode-trapping properties of the new models differ significantly from those characterizing the ZZ Ceti models of our previous works, particularly for long periods. Conclusions. The improvements in the modeling of ZZ Ceti stars we present here lead to substantial differences in the predicted pulsational properties of ZZ Ceti stars, which are expected to impact the asteroseismological inferences of these stars. This is extremely relevant in view of the abundant amount of photometric data from current and future space missions, resulting in discoveries of numerous ZZ Ceti stars.

The VMC survey – XLVI. Stellar proper motions in the centre of the Large Magellanic Cloud

ABSTRACT We present proper motion (PM) measurements within the central region of the Large Magellanic Cloud (LMC), using near-infrared data from the VISTA survey of the Magellanic Cloud system (VMC). This work encompasses 18 VMC tiles covering a total sky area of ∼28 deg2. We computed absolute stellar PMs from multiepoch observations in the Ks filter over time baselines between ∼12 and 47 months. Our final catalogue contains ∼6322 000 likely LMC member stars with derived PMs. We employed a simple flat-rotating disc model to analyse and interpret the PM data. We found a stellar centre of rotation ($\alpha _{0} = 79.95^{\circ }\,^{+0.22}_{-0.23}$, $\delta _0 = -69.31^{\circ }\,^{+0.12}_{-0.11}$) that is in agreement with that resulting from Hubble Space Telescope data. The inferred viewing angles of the LMC disc ($i=33.5^{\circ }\,^{+1.2}_{-1.3}$, $\Theta =129.8^{\circ }\,^{+1.9}_{-1.9}$) are in good agreement with values from the literature but suggest a higher inclination of the central parts of the LMC. Our data confirm a higher rotation amplitude for the young (≲0.5 Gyr) stars compared to the intermediate-age/old (≳1 Gyr) population, which can be explained by asymmetric drift. We constructed spatially resolved velocity maps of the intermediate-age/old and young populations. Intermediate-age/old stars follow elongated orbits parallel to the bar’s major axis, providing first observational evidence for x1 orbits within the LMC bar. In the innermost regions, the motions show more chaotic structures. Young stars show motions along a central filamentary bar structure.

Non-linear tidal excitation of superharmonic gravity waves in main-sequence stars in binary and exoplanetary systems

ABSTRACT We study the role of non-linear effects on tidally excited internal gravity waves in stellar radiation zones in exoplanetary or binary systems. We are partly motivated to study tides due to massive short-period hot Jupiters, which preferentially orbit stars with convective cores, for which wave breaking near the stellar centre cannot operate. We develop a theory (and test it with numerical calculations) for the non-linear excitation of superharmonic ‘secondary’ waves (with frequencies 2ωp) by a ‘primary’ tidal wave (with frequency ωp) near the interface between the radiation zone and convective envelope. These waves have the same horizontal phase speeds to leading order, and this non-linear effect could contribute importantly to tidal dissipation if the secondary waves can efficiently damp the primary. We derive criteria involving the orbital and stellar parameters required to excite these secondary waves to large amplitudes using a local model of the radiative/convective interface, which we convert to apply to tides in a spherical star. We numerically evaluate the critical amplitudes required for this new non-linear effect to become important using stellar models, comparing them to the ‘conventional’ criteria for wave breaking in radiative cores and the application of WKBJ theory near convective cores. The criteria for this new effect are easier to satisfy than the conventional measures of non-linearity in 1.4 and $2\, {\rm M}_\odot$ stars on the main sequence. We predict non-linear effects to be important even for planetary-mass companions around the latter, but this effect is probably less important in stars with radiative cores.

Off-centred force-free neutron star magnetospheres

ABSTRACT Neutron star electromagnetic activity produces pairs that fill their magnetosphere represented to the zeroth order by the force-free approximation. Neither dissipation nor acceleration nor radiation from charged particles is expected from this simplified model. So far, only centred dipole magnetic fields have been studied in this limit. In this paper, we explore the consequences of a rotating off-centred dipole on the force-free magnetosphere, showing the new magnetic field geometry, its spin-down luminosity, and the electromagnetic kick and torque felt by the neutron star. Solutions are obtained by time-dependent numerical simulations of the force-free regime using our pseudo-spectral code written in spherical coordinates. Our results are also compared to known analytical expressions found for the off-centred vacuum dipole by an expansion to lowest order in the parameter ϵ = d/R, where d is the displacement of the dipole from the stellar centre and R the neutron star radius. The presence of a force-free plasma enhances the spin-down luminosity and the electromagnetic kick and torque with respect to a centred force-free dipole. The impact on isolated and binary neutron stars is revised in light of these new results.

Magnetic quadri-dipolar stars rotating in vacuum

ABSTRACT Main-sequence stars and compact objects such as white dwarfs and neutron stars are usually embedded in magnetic fields that strongly deviate from a pure dipole located right at the stellar centre. An off-centred dipole can sometimes better adjust existing data and offer a simple geometric picture to include multipolar fields. However, such configurations are usually to restrictive, limiting multipolar components to strength less than the underlying dipole. In this paper, we consider the most general lowest order multipolar combination given by a dipole and a quadrupole magnetic field association in vacuum. Following the general formalism for multipolar field computations, we derive the full electromagnetic field outside a rotating quadridipole. Exact analytical expressions for the Poynting flux and the electromagnetic kick are given. Such geometry is useful to study the magnetosphere of neutron stars for which more and more compelling observations reveals hints for at least quadridipolar fields. We also show that for sufficiently high quadrupole components at the stellar surface, the electromagnetic kick imprinted to a neutron star can reach thousands of km s−1 for a millisecond period at birth.

Non-radially pulsating stars as microlensing sources

ABSTRACT We study the microlensing of non-radially pulsating (NRP) stars. Pulsations are formulated for stellar radius and temperature using spherical harmonic functions with different values of l, m. The characteristics of the microlensing light curves from NRP stars are investigated in relation to different pulsation modes. For the microlensing of NRP stars, the light curve is not a simple multiplication of the magnification curve and the intrinsic luminosity curve of the source star, unless the effect of finite source size can be ignored. Three main conclusions can be drawn from the simulated light curves. First, for modes with m ≠ 0 and when the viewing inclination is more nearly pole-on, the stellar luminosity towards the observer changes little with pulsation phase. In this case, high-magnification microlensing events are chromatic and can reveal the variability of these source stars. Secondly, some combinations of pulsation modes produce nearly degenerate luminosity curves (e.g. (l, m) = (3, 0), (5, 0)). The resulting microlensing light curves are also degenerate, unless the lens crosses the projected source. Finally, for modes involving m = 1, the stellar brightness centre does not coincide with the coordinate centre, and the projected source brightness centre moves in the sky with pulsation phase. As a result of this time-dependent displacement in the brightness centroid, the time of the magnification peak coincides with the closest approach of the lens to the brightness centre as opposed to the source coordinate centre. Binary microlensing of NRP stars and in caustic-crossing features are chromatic.

Impact of an off-centred dipole on neutron star binaries

ABSTRACT Neutron stars are strongly magnetized rotating compact objects. Therefore, they also produce huge electric fields accelerating particles to ultrarelativistic energies. The simplest magnetic topology is a dipole traditionally located at the stellar centre. In this paper, we re-investigate the consequences of an off-centred rotating magnetic dipole, showing accurate magnetic field line geometries, the associated spin-down luminosity as well as the corresponding electromagnetic kick and torque imprinted to the neutron star. Results are obtained by time-dependent numerical simulations of Maxwell equations in vacuum using pseudo-spectral methods. We compare our results to known analytical expressions available to lowest order in the parameter ϵ = d/R, where d is the displacement of the dipole from the stellar centre and R the neutron star radius. We found good agreement between our numerical computations and our analytical approximations even for well off-centred dipoles having large displacements with a sizeable fraction of the radius, i.e. ϵ ≲ 1. An explanation for binary neutron star eccentricity distribution functions is given with an emphasize on highly eccentric systems as an alternative scenario to traditional binary formation.

Thawing the frozen-in approximation: implications for self-gravity in deeply plunging tidal disruption events

ABSTRACT The tidal destruction of a star by a massive black hole, known as a tidal disruption event (TDE), is commonly modelled using the ‘frozen-in’ approximation. Under this approximation, the star maintains exact hydrostatic balance prior to entering the tidal sphere (radius rt), after which point its internal pressure and self-gravity become instantaneously negligible and the debris undergoes ballistic free fall. We present a suite of hydrodynamical simulations of TDEs with high penetration factors β ≡ rt/rp = 5−7, where rp is the pericentre of the stellar centre of mass, calculated using a Voronoi-based moving-mesh technique. We show that basic assumptions of the frozen-in model, such as the neglect of self-gravity inside rt, are violated. Indeed, roughly equal fractions of the final energy spread accumulate exiting and entering the tidal sphere, though the frozen-in prediction is correct at the order-of-magnitude level. We also show that an $\mathcal {O}(1)$ fraction of the debris mass remains transversely confined by self-gravity even for large β which has implications for the radio emission from the unbound debris and, potentially, for the circularization efficiency of the bound streams.

Wandering off the centre: a characterization of the random motion of intermediate-mass black holes in star clusters

Despite recent observational efforts, unequivocal signs for the presence of intermediate-mass black holes (IMBHs) in globular clusters (GCs) have not been found yet. Especially when the presence of IMBHs is constrained through dynamical modeling of stellar kinematics, it is fundamental to account for the displacement that the IMBH might have with respect to the GC centre. In this paper we analyse the IMBH wandering around the stellar density centre using a set of realistic direct N-body simulations of star cluster evolution. Guided by the simulation results, we develop a basic yet accurate model that can be used to estimate the average IMBH radial displacement ($\left<r_\mathrm{bh}\right>$) in terms of structural quantities as the core radius ($r_\mathrm{c}$), mass ($M_\mathrm{c}$), and velocity dispersion ($\sigma_\mathrm{c}$), in addition to the average stellar mass ($m_\mathrm{c}$) and the IMBH mass ($M_\mathrm{bh}$). The model can be expressed by the equation $\left<r_\mathrm{bh}\right>/r_\mathrm{c}=A(m_\mathrm{c}/M_\mathrm{bh})^\alpha[\sigma_\mathrm{c}^2r_\mathrm{c}/(GM_\mathrm{c})]^\beta$, in which the free parameters $A,\alpha,\beta$ are calculated through comparison with the numerical results on the IMBH displacement. The model is then applied to Galactic GCs, finding that for an IMBH mass equal to 0.1% of the GC mass, the typical expected displacement of a putative IMBH is around $1''$ for most Galactic GCs, but IMBHs can wander to larger angular distances in some objects, including a prediction of a $2.5''$ displacement for NGC 5139 ($\omega$ Cen), and $>10''$ for NGC 5053, NGC 6366 and ARP2.

Radiation from an off-centred rotating dipole in vacuum

When a neutron star forms, after the collapse of its progenitor, a strong magnetic field survives in its interior. This magnetic topology is usually assumed to be well approximated by a dipole located right at the centre of the star. However, there is no particular reason why this dipole should be attached to this very special point. A slight shift from the stellar centre could have strong implications for the surrounding electromagnetic field configuration leading to clear observational signatures. We study the effect of the most general off-centred dipole anchored in the neutron star interior. Exact analytical solutions are given in vacuum outside the star to any order of accuracy in the small parameter $\epsilon = d/R$, where $d$ is the displacement of the dipole from the stellar centre and $R$ the neutron star radius. As a simple diagnostic of this decentred dipole, the spin-down luminosity and the torque exerted on its crust are computed to the lowest leading order in~$\epsilon$. Results are compared to earlier works and a discussion on repercussions on pulsar braking index and multi-wavelength light curves is proposed.

Core-envelope and regular models in Einstein-Maxwell fields

New classes of exact solutions which could serve as sources for the Reissner-Nordstrom metric representing the exterior gravitational field of an isolated charged sphere are derived. Firstly, we sacrifice the requirement that the stellar centre is free of a singularity and then obtain a core-envelope model. The charged fluid envelope is matched suitably to the neutral core and the vacuum exterior solution. Next we investigate models of charged stars that are regular at the stellar centre. The Einstein-Maxwell system of partial differential equations is reduced to the study of a single first-order differential equation in which two of the matter or geometrical variables must be specified at the outset. In each case mentioned above, new exact models are found by choosing functional forms for the electric field intensity and one of the gravitational potentials. A Riccati equation is then solved to obtain the remaining potential. The charged spherical shell model as well as the non-singular models are shown to display necessary qualitative features that are demanded for physical acceptability. It is shown that the regular model has a vanishing pressure-free hypersurface. The density and pressure profiles are positive and monotonically decreasing outwards from the centre of the sphere for a chosen set of parameters. The weak strong and dominant energy conditions are also satisfied. A drawback of the model is that the causality criterion is not satisfied within the fluid boundary.

MODEL OF DEGENERATE DWARF WITH SPIN-POLARIZED ELECTRON SYSTEM

A three-parametric model of a massive degenerate dwarf was proposed. Unlike paramagnetic state of electron system in the standard Chandrasekhar model electrons are considered in a partially spin-polarized state. The parameters of the model are: x 0 – the relativism parameter at stellar centre, μ e = – the average chemical composition parameter and ζ – the degree of spin polarization of the electron system. The macroscopic characteristics (e.g. mass, radius, energy) as functions of the model parameters were obtained from the solution of the mechanical equilibrium equation. The electron spin polarization was shown to lead to the increase of stellar radius and especially to mass compared with the corresponding characteristics of the standard model. The application of the proposed model to interpreting the stability of massive dwarfs in binary system was discussed.

A unified normal mode approach to dynamic tides and its application to rotating Sun-like stars

We determine the response of a uniformly rotating star to tidal perturbations due to a companion. General periodic orbits and parabolic flybys are considered. We evaluate energy and angular momentum exchange rates as a sum of contributions from normal modes allowing for dissipative processes. We consider the case when the response is dominated by the contribution of an identifiable regular spectrum of low-frequency modes, such as rotationally modified gravity modes. We evaluate this response in the limit of very weak dissipation, where individual resonances can be significant and also when dissipative effects are strong enough to prevent wave reflection from the neighbourhood of either the stellar surface or stellar centre, making radiation conditions more appropriate. The former situation may apply to Sun-like stars with radiative cores and convective envelopes and the latter to more massive stars with convective cores and radiative envelopes. We provide general expressions for transfer of energy and angular momentum that can be applied to an orbit with any eccentricity. Detailed calculations require knowledge of the mode spectrum and evaluation of the mode overlap integrals that measure the strength of the tidal interaction. These are evaluated for Sun-like stars in the slow rotation regime where centrifugal distortion is neglected in the equilibrium and the traditional approximation is made for the normal modes. We use both a Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) procedure and a direct numerical evaluation which are found to be in good agreement for regimes of interest. The former is used to provide expressions for the mode spectrum and overlap integrals as a function of mode frequency and stellar rotation rate. These can be used to find the tidal energy and angular momentum exchange rates and hence the orbital evolution. Finally we use our formalism to determine the evolution time scales for an object, in an orbit of small eccentricity, around a Sun-like star in which the tidal response is assumed to occur. Systems with either no rotation or synchronous rotation are considered. Only rotationally modified gravity modes are taken into account under the assumption that wave dissipation proceeds close to the stellar centre. It is noted that inertial waves excited in the convective envelope may produce a comparable amount of tidal dissipation in the latter case for sufficiently large orbital periods.

Compact models with regular charge distributions

We model a compact relativistic body with anisotropic pressures in the presence of an electric field. The equation of state is barotropic with a linear relationship between the radial pressure and the energy density. Simple exact models of the Einstein-Maxwell equations are generated. A graphical analysis indicates that the matter and electromagnetic variables are well behaved. In particular the proper charge density is regular for certain parameter values at the stellar centre unlike earlier anisotropic models in the presence of charge. We show that the electric field affects the mass of stellar objects and the observed mass for a particular binary pulsar is regained. Our models contain previous results of anisotropic charged matter with a linear equation of state for special parameter values.

Regular models with quadratic equation of state

We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein-Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.

Impact of rotation and disc lifetime on pre-main sequence lithium depletion of solar-type stars

Aims: We study the influence of rotation and disc lifetime on lithium depletion of pre-main sequence (PMS) solar-type stars. Methods: The impact of rotational mixing and of the hydrostatic effects of rotation on lithium abundances are investigated by computing non-rotating and rotating PMS models that include a comprehensive treatment of shellular rotation. The influence of the disc lifetime is then studied by comparing the lithium content of PMS rotating models experiencing different durations of the disc-locking phase between 3 and 9 Myr. Results: The surface lithium abundance at the end of the PMS is decreased when rotational effects are included. During the beginning of the lithium depletion phase, only hydrostatic effects of rotation are at work. This results in a decrease in the lithium depletion rate for rotating models compared to non-rotating ones. When the convective envelope recedes from the stellar centre, rotational mixing begins to play an important role due to differential rotation near the bottom of the convective envelope. This mixing results in a decrease in the surface lithium abundance with a limited contribution from hydrostatic effects of rotation, which favours lithium depletion during the second part of the PMS evolution. The impact of rotation on PMS lithium depletion is also found to be sensitive to the duration of the disc-locking phase. When the disc lifetime increases, the PMS lithium abundance of a solar-type star decreases owing to the higher efficiency of rotational mixing in the radiative zone. A relationship between the surface rotation and lithium abundance at the end of the PMS is then obtained: slow rotators on the zero-age main sequence are predicted to be more lithium-depleted than fast rotators due to the increase in the disc lifetime.

Arp 220: EXTINCTION AND MERGER-INDUCED STAR FORMATION

We analyse new spatially resolved integral field spectroscopic H- and K-band data at a resolution of 0.3arcsec (100pc) and re-analyse interferometric CO(2-1) line observations of the prototypical merging system Arp220. We find that the majority of the K-band luminosity is due to a 10Myr old starburst, with a significant contribution from an underlying ca 1Gyr old stellar population, and a small contribution from stars less than 8Myr old. The Calzetti (2000) reddening law provides the best fit to photometric datapoints spanning 0.45um -- 2.12um. Furthermore, estimates of the bolometric luminosity from IRAS fluxes in conjunction with our stellar population analysis indicate that we observe less than 10% of the emitted K-band light. The stellar and CO(2-1) kinematic centre of the western nucleus coincides with the compact hot dust emission, indicating that the latter marks the centre of the gravitational potential. In the eastern nucleus, the CO(2-1) data are well matched by a model in which the gas orbits around the peak of the dust emission. This, and the similarity of the K-band tracer kinematics, shows that despite the irregular morphology, the eastern nucleus is also a kinematically coherent structure. Comparison of the extinction map and EW_CO and EW_Br-gamma maps indicates that the lower half of the eastern nucleus is significantly more extincted than the upper half, suggesting that the lower half is buried in the larger-scale gas disk.

Implications of primordial black holes on the first stars and the origin of the super-massive black holes

If the cosmological dark matter has a component made of small primordial black holes (BHs), they may have a significant impact on the physics of the first stars and on the subsequent formation of massive BHs. Primordial BHs would be adiabatically contracted into these stars and then would sink to the stellar centre by dynamical friction, creating a larger BH which may quickly swallow the whole star. If these primordial BHs are heavier than ∼1022 g, the first stars would likely live only for a very short time and would not contribute much to the reionization of the Universe. They would instead become 10–103 M⊙ BHs which (depending on subsequent accretion) could serve as seeds for the super-massive BHs seen at high redshifts as well as those inside galaxies today.

Generalized isothermal models with strange equation of state

We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal universe. We show that the mass corresponds to values obtained previously for quark stars when anisotropy and charge are present.